let GF be non empty right_complementable associative well-unital distributive Abelian add-associative right_zeroed doubleLoopStr ; :: thesis: for V being non empty right_complementable VectSp-like Abelian add-associative right_zeroed VectSpStr of GF
for W being Subspace of V holds the carrier of W is Coset of W
let V be non empty right_complementable VectSp-like Abelian add-associative right_zeroed VectSpStr of GF; :: thesis: for W being Subspace of V holds the carrier of W is Coset of W
let W be Subspace of V; :: thesis: the carrier of W is Coset of W
the carrier of W = (0. V) + W by Lm3;
hence the carrier of W is Coset of W by Def6; :: thesis: verum